where \(\mathbf {C}^{\mathrm {LMO}}\)  is the \((N_{\mathrm {c}}+N_{\mathrm {a}}+N_{\mathrm {v}})\) -dimensional coefficient matrix of the molecular ROHF LMOs in the basis \(\lbrace \chi _{\mu }\rbrace \)  and \(\mathbf {B}_{\mathrm {x}}^{\mathrm {LMO}}\)  is a \(K_{\mathrm {x}}\times N_{\mathrm {x}}\)  rectangular matrix.
For each row of \(\mathbf {B}_{\mathrm {x}}^{\mathrm {LMO}}\) , one can identify the largest matrix element so as to form a closed
\(K_{\mathrm {x}}\times K_{\mathrm {x}}\)  subblock. In particular, \(B_{\mathrm {a}}^{\mathrm {LMO}}\)  should be a strongly diagonal \(K_{\mathrm {a}}\times K_{\mathrm {a}}\)  matrix,
with all diagonal elements close to one. Otherwise, the occupations of the pre-CMOs must be reassigned until this criterion is fulfilled.
As a matter of fact, for most organic systems, the \(K_{\mathrm {c}}\times K_{\mathrm {c}}\)  subblock of \(B_{\mathrm {c}}^{\mathrm {LMO}}\)  and
the \(K_{\mathrm {v}}\times K_{\mathrm {v}}\)  subblock of \(B_{\mathrm {v}}^{\mathrm {LMO}}\)  are also strongly diagonal, as can be seen from
Tables REF  and REF  for
the case of (C4SH3)-(CH2)10-(C4SH3) (see Ref. DLPNO-NEVPT2 for the geometry).
Actually, following the maximum occupation method (mom) for excited solutions of the HF equation[1]},
an occupation number \(n_i\)  can be defined for each molecular LMO \(\psi _i^{\mathrm {LMO}}\)  in the space spanned by the pre-LMOs,
\(n_{\mathrm {x},i}&=&\langle \psi _{\mathrm {x},i}^{\mathrm {Y}}|P_{\mathrm {x}}^{\mathrm {Y}}|\psi _{\mathrm {x},i}^{\mathrm {Y}}\rangle =\sum _{p\in \mathrm {x}}^{K_{\mathrm {x}}}[(B_{\mathrm {x}}^{\mathrm {Y}})_{pi}]^2,\quad \mathrm {x}=\mathrm {a}, \mathrm {c}, \mathrm {v}; \quad \mathrm {Y}=\mathrm {LMO}, \mathrm {CMO},\\P_{\mathrm {x}}^{\mathrm {Y}}&=&\sum _{p\in \mathrm {x}}^{K_{\mathrm {x}}}|\tilde{\psi }_{\mathrm {x},p}^{\mathrm {Y}}\rangle \langle \tilde{\psi }_{\mathrm {x},p}^{\mathrm {Y}}|,\) 
